Square of `(3x - 5xy)` is

Options

A. `9x ^(2)-30 x ^(2) y + 25 x ^(2) y ^(2)`
B. `9x ^(2) - 15 x ^(2) y + 25 x ^(2) y ^(2)`
C. `25 x ^(2) - 15 x ^(2) y + 25 x ^(2) y ^(2)`
D. `25 x ^(2) - 30 x ^(2) y + 9x ^(2) y ^(2)`

Answer

To find the square of the expression \( (3x - 5xy) \), we can use the formula for the square of a binomial, which is:

\[ (a - b)^2 = a^2 - 2ab + b^2 \]

Here, we can identify:
- \( a = 3x \)
- \( b = 5xy \)

Now, we can apply the formula step by step.

### Step 1: Calculate \( a^2 \)
\[ a^2 = (3x)^2 = 9x^2 \]

### Step 2: Calculate \( b^2 \)
\[ b^2 = (5xy)^2 = 25x^2y^2 \]

### Step 3: Calculate \( 2ab \)
\[ 2ab = 2 \cdot (3x) \cdot (5xy) = 30x^2y \]

### Step 4: Combine all parts using the formula
Now, substituting \( a^2 \), \( b^2 \), and \( 2ab \) into the formula:
\[ (3x - 5xy)^2 = a^2 - 2ab + b^2 \]
\[ = 9x^2 - 30x^2y + 25x^2y^2 \]

### Final Answer
Thus, the square of \( (3x - 5xy) \) is:
\[ 9x^2 - 30x^2y + 25x^2y^2 \]

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